Toward Practical Forecasts of Public Sentiments via Convexification for Mean Field Games: Evidence from Real World COVID-19 Discussion Data

TL;DR

This work demonstrates the practical viability of forecasting public sentiment with a convexification-based solver for Mean Field Games, using real-world COVID-19 Twitter data. By formulating a coupled HJB-FPK MFG system and applying Carleman-weighted convexification, the authors obtain globally convergent solutions that closely align with observed sentiment densities while satisfying the governing equations. The study presents a thorough proof-of-concept with periodized calibration of coefficients and initial data, highlighting both the promise and current limitation of manual parameter identification. The results suggest MFG-based sentiment forecasting can capture complex temporal patterns, laying groundwork for systematic coefficient identification and higher-dimensional sentiment modeling. This approach offers a principled alternative to purely data-driven forecasting for crisis management and public health planning.

Abstract

We apply a convexification-based numerical method to forecast public sentiment dynamics using Mean Field Games (MFGs). The theoretical foundation for the convexification approach, established in our prior work, guarantees global convergence to the unique solution to the MFG system. The present work demonstrates the practical potential of this framework using real-world sentiment data extracted from social media public discussion during the COVID-19 pandemic. The results show that the MFG model with appropriate parameters and convexification yields sentiment density predictions that align closely with observed data and satisfy the governing equations. While current parameter selection relies on manual calibration, our findings establish the first proof-of-concept evidence that MFG models can capture complex temporal patterns in public sentiment, laying the groundwork for future work on systematic parameter identification methods, i.e. solutions of coefficient inverse problems for the MFG system.

Figures (11)

• Figure 1: Sentiment distributions of public discussions on COVID-19 across four consecutive weeks from March 2 to March 29, 2020. Each subplot displays the histogram of VADER compound sentiment scores for the corresponding week, overlaid with a KDE fit curve shown in solid blue. The distributions reveal temporal variations in sentiment polarity and dispersion during the early stage of the pandemic. Note: the histograms have been normalized to represent the density of sentiment scores in each of the four weeks, not the original counts.
• Figure 2: Convexification solution versus observed sentiment densities for weeks 6--8 in Period 7. The blue curve represents the convexification solution, while the red curve represents the observed data.
• Figure 3: The true cost \ref{['true_cost']} for Period 1.
• Figure 4: Error metric \ref{['error_metric']} for Period 1. Each tile's color represents the metric value for the corresponding week and sentiment. Dark blue tiles are where the metric is smallest, while dark red tiles are where the metric is largest.
• Figure 5: Period 1: March 2 to May 17, 2020.

Theorems & Definitions (8)

• Remark 2.1
• Theorem 3.1
• Theorem 3.3
• Theorem 3.4
• Remark 5.1
• Remark 5.2
• Remark 6.1
• Remark 6.2